This paper deals with a robust H₂ output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H₂ norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) and a multimachine power system. The simulation results illustrate the effectiveness and robustness of the proposed stabilizer over a wide range of loading conditions.